There are many interesting aspects of chaos, and entropy for example is one of them. How do the two relate? Chaos is measured by means of entropy. But what is entropy? Nothing new. Entropy has always been here. There. Everywhere. And it only took a smart physicist to have given entropy a name and a definition. So it came to the great Clausius that he identified the entropy S as a significant quantity. Let me try and explain entropy to you. I suppose you know what a physical system is. Entropy (thermodynamic) describes two things: 1) the amount of energy in a physical system which cannot be used to do work, 2) the disorder of the system, i.e. the measure of chaos.

Also note: a) When somebody tells you that you have done nothing but increased the overall entropy, you can calmly respond: We all do that, increase the entropy, all the time, with everything we do. b) Making order somewhere necessarily means making a bigger mess somewhere else. c) Entropy in the context of computers, mathematics, biology and linguistic signifies something different, but analogous. d) In 19th century, a popular scientific notion suggested that entropy was gradually increasing, and therefore the universe was running down and eventually all motion would cease. When people realized that this would not happen for billions of years, if it happened at all, concern about this notion generally disappeared.

Let me explain Note b in the context of tidying my room. It is tidy at the moment, yet it can be very messy. I don't like my room to be messy. It is my abode! So I clean it regularly. When I do this, I organize things: sort clothes, papers, books, stationery, clean the dust. I throw away items absolutely unnecessary. My room shines. And that's great. I can only function in order. I put the entropy of my room down to a satisfactory level. Aha, I put it down. Can I do that? Yes I can, at least in my room. And here lies the catch: I made my room to be the isolated system. And its entropy lowered. But had I been fair, I should've also inspected the systems which I interacted with. I should've at least: - looked into the dust bins I've filled, or even further - the rubbish dump, - looked into the rooms around the house, where I discarded those things not absolutely unnecessary, but just sort of unwanted in my room at the moment. (I am sure you know what I am talking about.)

Now if I had counted all these things and recalculated the change in entropy, it would've probably increased. Or maybe I should've also taken into account the room of my girl-friend, for she was so jealous of my tidy room she abruptly rushed home to have done the same with hers. Or maybe my whole home-town, since ... now that I come to think about it: home-town is not enough, even the Earth is not enough. Earth is not an isolated system. System should be as big as the Universe, which is probably the largest thing there is. Entropy of an isolated physical system increases whatever we do. Entropy stays the same only if we do: - something very very quietly - reversibly and cyclically so to speak, - or absolutely nothing, no breathing, no peaking, nothing.

Since its discovery, the idea that disorder tends to increase has been the focus of a great deal of thought, some of it confused. A chief point of confusion is the fact that the inevitable increase in entropy applies only to isolated systems; notably, the Earth is not an isolated system because it is constantly receiving energy in the form of sunlight. Meanwhile, in an expanding universe, some believe the maximum possible entropy increases far more quickly than the actual entropy with each time increment, pushing the universe continually further away from an equilibrium state despite increasing entropy.

Nobody can do much about the entropy increasing. In fact the more you try, the faster the entropy increases. So the only sensible thing you can do is to adapt. Some people like the idea of entropy constantly increasing. They also enjoy sex, and life in general: their cars, and filling them with fuel; wrapping up Christmas presents, making cookies, cleaning their houses; and so on. However there are some who, although they crave those things - sex, life and music -, are just too depressed, lazy or crazy to do anything about winning them. So most of the time they think life is a bore, that increasing the entropy is a bad thing. Pessimists they are called. There are also others - who are even in the majority - who don't care about entropy whatsoever, and most of them probably don't have a clue about its meaning either. Are they pessimists or optimist, who can tell. They are definitely ignorant of science. But that is not for us to regret. The entropy is here. It will still be here tomorrow, and always increasing, always waiting to be studied. Do you recall Andy Dufrense from Shawshank Redemption? Andy Dufresne who crawled through a river of shit and came out clean on the other side. To order through disorder - I guess there is no way around. And though loony, lovely and true is that journey!

The picture above shows the art (my favorite) of M.C. Escher: Reptiles it is called. It shows the life cycle of a little alligator. Amid a mosaic of reptilian figures it is he who is evidently tired of lying flat and rigid amongst his fellows, so he puts one plastic-looking leg over the edge of the book, wrenches himself free and launches out into real life. On the way to the highest point of his existence. Then after a quick snort, tired but fulfilled, he goes downhill again, via an ashtray, to the level surface, to that flat drawing paper, and meekly rejoins his erstwhile friends, taking up once more his function as an element of surface division.

Even though I studied the theory of chaos to a great deal at university, I was glad to have come across this book. Chaos tells many stories in a strictly down-to-earth manner: how chaos came to be understood, mathematized etc., so I guess just about anybody can appreciate the subject.